Paul Erdös was a prolific and eccentric mathematician (see BodyMods (23 December 1999)). There's a graph-theoretic recreation inspired by his career: assign anybody who co-authored a paper with Erdös an Erdös Number 1. Award an Erdös Number 2 to anybody who co-authored with a co-author of Erdös. And so forth....

What's the distribution of Erdös Numbers? That's an interesting question, associated with the "small worlds" phenomena discussed under the label of "social network analysis", aka SNA. How are people connected to one another? Some folks are loners and associate rarely. Others are promiscuous but only within a particular sub-culture. Still others are ecletic and bridge gaps between diverse groups. The "Six Degrees of Kevin Bacon" game shows how analogous links work between movie actors.

Now, to get personal: if one allows non-mathematicians to have Erdös Numbers based on papers published in scientific journals, then what's my Number? I tried to figure it out some years ago, with the help of an Erdös Number expert. For a while we thought it might be as small as 3, based on a chain from Erdös co-author S. J. Kovacs to Kip Thorne to yours truly. But that turned out to be a case of mistaken identity: the Sandor J. Kovacs who was a fellow grad student in Kip's group was not the S. J. Kovacs of the math world.

So, given no unexpected new joint publications, I now believe that my Erdös Number is probably 5. That estimate is based on unconfirmed but likely links between my physics co-authors to varied mathematical physicists to various pure mathematicians to Erdös colleagues. It's a small world ....